Ideally, you want turnips to be as cold as possible without freezing, and that means putting them in the coldest parts of the fridge. That's the crisper drawer or the bottom shelf, and they'll ...

Main-crop turnips will keep in a cool, dark place for much longer. To freeze early-crop turnips, trim, peel and dice them, then blanch, cool and pack into freezer bags. Cook from frozen.